Answer:
B, 2100
Step-by-step explanation:
For the given function f(t) = (2t + 1) using definition of Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
As given in the question,
Given function is equal to :
f(t) = 2t + 1
Simplify the given function using definition of Laplace transform we have,
L(f(t))s = 
= ![\int\limits^\infty_0[2t +1] e^{-st} dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cinfty_0%5B2t%20%2B1%5D%20e%5E%7B-st%7D%20dt)
= 
= 2 L(t) + L(1)
L(1) = 
= (-1/s) ( 0 -1 )
= 1/s , ( s > 0)
2L ( t ) = 
= ![2[t\int\limits^\infty_0 e^{-st} - \int\limits^\infty_0 ({(d/dt)(t) \int\limits^\infty_0e^{-st} \, dt )dt]](https://tex.z-dn.net/?f=2%5Bt%5Cint%5Climits%5E%5Cinfty_0%20e%5E%7B-st%7D%20-%20%5Cint%5Climits%5E%5Cinfty_0%20%28%7B%28d%2Fdt%29%28t%29%20%5Cint%5Climits%5E%5Cinfty_0e%5E%7B-st%7D%20%5C%2C%20dt%20%29dt%5D)
= 2/ s²
Now ,
L(f(t))s = 2 L(t) + L(1)
= 2/ s² + 1/s
Therefore, the solution of the given function using Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
Learn more about Laplace transform here
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Answer:
Step-by-step explanation:
a) The probability that the hand contains exactly one ace
No of ways of selecting one ace and four non ace would be
=
i.e. α=778320
b) the probability that the hand is a flush
No of ways of getting a flush is either all 5 hearts or clubs of spades or dice
= 
ie. β=5148
c) the probability that the hand is a straight flush
In each of the suit to get a straight flush we must have either A,2,3,4,5 or 2,3,4,5,6, or .... or 9,10, J, q, K
So total no of ways = 
γ=46332
Answer:
n= -4
Step-by-step explanation:
First we have to find the equation of line which passes through (6,3) and (8,4).
Then we have to pass this line through the point (n , -2).
we know, equation of line passing through (x1,y1) and (x2,y2) is

So, the equation of line passing through (6,3) and (8,4) is

or, 
multiplying both sides by -2
x-6=2(y-3)
or, x-6=2y-6
or, x-2y=6-6
or, x-2y=0
Now, we have to pass this line through (n,-2)
So, using the point in the line, that is using x=n , y=-2
we get
n-2(-2)=0
or, n+4=0
or, n=-4
Answer:
(10,6)
Step-by-step explanation:
The equation you would use to solve this is (x1+x2/2 , y1+y2/2) so when you plug in the numbers you get this (6+14/2 , 3+9/2) which eventually simplifies into (10, 6)